Rinkevičius graduated from Lithuania's M. K. Čiurlionis School of Arts, from the Saint Petersburg Conservatory in 1983, and from Moscow State Tchaikovsky Conservatory in 1986. In 1985 he was won the Herbert von Karajan Fund International Competition for Conductors in Berlin. Between 1996 and 2003, he served as the Latvian National Opera’s artistic director and chief conductor; he was also chief conductor at the Malmö Opera and Music Theatre from 2002 to 2005.
Among the symphony orchestras he has conducted are the Berliner Symphoniker, the Weimar Staatskapelle, the Copenhagen Tivoli Symphony, the St Petersburg Philharmonic Orchestra, the Russian National Symphony, and the Russian State Symphony. He has conducted performances in Salzburg, the Royal Albert Hall in London, and the Champs Elysées Theatre in Paris, as well as in Taiwan and Hong Kong. He has been a featured conductor at the Bolshoi Theatre in Moscow since 2003.
Rinkevičius continues to work in Lithuania, staging operas at the Lithuanian National Opera and Ballet Theatre, serving as chief conductor and artistic director of the Lithuanian State Symphony Orchestra, and as a professor at the Lithuanian Academy of Music and Theatre. He has used these opportunities to introduce a number of original compositions by Lithuanian composers, including A Letter to all the Congregation by Algirdas Martinaitis and Agnus Dei by Feliksas Bajoras.
Since September 2007 Gintaras Rinkevičius is also an artistic director and principal conductor of the Novosibirsk Academic Symphony Orchestra.